Comparing correlations between two variables across subgroups

[Konstantinos Ioannidis]

I have the following experimental design. I have two continuous variables per subject, call them X and Y. Subjects are separated in four groups based on levels of a categorical variable, call it Z. My hypothesis is that the Corr(X,Y) will be different within each levels of Z. More specifically, I believe it will be monotonically increasing. Hence, I am mainly interested to test whether the correlation between X and Y differs across levels of Z. I have some predictions for the magnitude of the correlations across Z from the literature; they should be around 0.02, 0.20, 0.28, 0.35. Of secondary interest are pairwise comparisons of correlations in adjacent levels of Z.

I want to find the most powerful statistical approach for this comparison as I want to have a full power analysis to compute sample size needed before I collect any data. I thought of using

 mvtest correlations X Y, by(Z)

but unclear how to compute sample size for it. I also thought of using

regress X c.Y##i.Z

but again unclear how to compute the sample size for this, especially since it is an interaction between a continuous and a categorical variable with more than two levels, so it is essentially multiple coefficients. There may be a simpler approach that did not cross my mind yet.

Appreciate any help.
Cheers!